{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sequential Monte Carlo with two gaussians"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running on PyMC3 v3.7\n"
     ]
    }
   ],
   "source": [
    "import pymc3 as pm\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import theano.tensor as tt\n",
    "import shutil\n",
    "\n",
    "plt.style.use('seaborn-darkgrid')\n",
    "print('Running on PyMC3 v{}'.format(pm.__version__))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sampling from $n$-dimensional distributions with multiple peaks with a standard Metropolis-Hastings algorithm can be difficult, if not impossible, as the Markov chain often gets stuck in either of the minima.\n",
    "\n",
    "A Sequential Monte Carlo sampler (SMC) is a way to overcome this problem, or at least to ameliorate it. SMC samplers are very similar to genetic algorithms, which are biologically-inspired algorithms that can be summarized as follows:\n",
    "\n",
    "1. Initialization: set a population of individuals\n",
    "2. Mutation: individuals are somehow modified or perturbed\n",
    "3. Selection: individuals with high _fitness_ have higher chance to generate _offspring_.\n",
    "4. Iterate by using individuals from 3 to set the population in 1.\n",
    "\n",
    "If each _individual_ is a particular solution to a problem, then a genetic algorithm will eventually produce good solutions to that problem. One key aspect is to generate enough diversity (mutation step) to explore the solution space avoiding getting trap in local minima and then apply _selection_ to _probabilistically_ keep reasonable solutions while also keeping some diversity. Being too greedy and short-sighted could be problematic, _bad_ solutions in a given moment could lead to _good_ solutions in the future.\n",
    "\n",
    "Moving into the realm of Bayesian statistics each individual is a point in the _posterior space_, mutations can be done in several ways, a general solution is to use a MCMC method (like Metropolis-Hastings) and run many Markov chains in parallel. The _fitness_ is given by the posterior, points with low posterior density will be removed and points high posterior density will be used as the starting point of a next round of Markov chains (This step is known as _reweighting_ in the SMC literature). The size of the population is kept fixed at some predefined value, so if a point is removed some other point should be used to start at least two new Markov chains.\n",
    "\n",
    "The previous paragraph is summarized in the next figure, the first subplot shows 5 samples (orange dots) at some particular stage. The second subplot shows how these samples are reweighted according to their posterior density (blue Gaussian curve). The third subplot shows the result of running a certain number of Metropolis steps, starting from the selected/reweighting samples in the second subplot, notice how the two samples with the lower posterior density (smaller circles) are discarded and not used to seed Markov chains.\n",
    "\n",
    "![SMC stages](https://github.com/pymc-devs/pymc3/raw/master/docs/source/notebooks/smc.png)\n",
    "\n",
    "So far we have that the SMC sampler is just a bunch of parallel Markov chains, not very impressive, right? Well not that fast. SMC proceed by moving _sequentially_ through a series of stages, starting from a simple to sample distribution until it get to the posterior distribution. All this intermediate distribution (or _tempered posterior distributions_) are controlled by _tempering_ parameter called $\\beta$. SMC takes this idea from other _tempering_ methods originated from a branch of physics known as _statistical mechanics_. The idea is as follow the number of accessible states a _real physical_ system can reach is controlled by the temperature, if the temperature is the lowest possible ($0$ Kelvin) the system is trapped in a single state, on the contrary if the temperature is $\\infty$ all states are equally accessible! In the _statistical mechanics_ literature $\\beta$ is know as the inverse temperature, the higher the more constrained the system is. Going back to the Bayesian statistics context a _natural_ analogy to these physical systems is given by the following formula:\n",
    "\n",
    "$$p(\\theta \\mid y)_{\\beta} \\propto p(y \\mid \\theta)^{\\beta} p(\\theta)$$\n",
    "\n",
    "When $\\beta = 0$, the _tempered posterior_ is just the prior and when $\\beta=1$ the _tempered posterior_ is the true posterior. SMC starts with $\\beta = 0$ and progress by always increasing the value of $\\beta$, at each stage, until it reach 1. This is represented in the avobe figure by a narrower Gaussian distribution in the third subplot.\n",
    "\n",
    "For the SMC version implemented in PyMC3 the number of chains is the number of draws. At each stage SMC will use independent Markov chains to explore the _tempered posterior_ (the black arrow in the figure). The final samples, _i.e_ those stored in the `trace`, will be taken exclusively from the final stage ($\\beta = 1$), i.e. the true posterior.\n",
    "\n",
    "The successive values of $\\beta$ are determined automatically from the sampling results of the previous intermediate distribution. SMC will try to keep the effective samples size (ESS) constant. Thus, the harder the distribution is to sample the larger the number of stages SMC will take. In other words the _cooling_ will be slow and the successive values of $\\beta$ will change in small steps.\n",
    "\n",
    "Two more parameters that are automatically determined are:\n",
    "* The number of steps each Markov chain takes to explore the _tempered posterior_ (`n_steps`) is determined from the acceptance rate at each stage, SMC use a _tune_interval_ to do this.\n",
    "* The width of the proposal distribution (`MultivariateProposal`) is also adjusted adaptively based on the  acceptance rate at each stage.\n",
    "\n",
    "\n",
    "Even when SMC uses the Metropolis-Hasting algorithm under the hood, it has several advantages over it:\n",
    "\n",
    "* It can sample from $n$-dimensional distributions with multiple peaks.\n",
    "* It does not have a burn-in period, it starts by sampling directly from the prior and then at each stage the starting points are already distributed according to the tempered posterior (due to the re-weighting step).\n",
    "* It is inherently parallel."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To see an example of how to use SMC inside PyMC3 let's define a multivariate gaussian of dimension $n$, their weights and the covariance matrix. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 4\n",
    "\n",
    "mu1 = np.ones(n) * (1. / 2)\n",
    "mu2 = -mu1\n",
    "\n",
    "stdev = 0.1\n",
    "sigma = np.power(stdev, 2) * np.eye(n)\n",
    "isigma = np.linalg.inv(sigma)\n",
    "dsigma = np.linalg.det(sigma)\n",
    "\n",
    "w1 = 0.1\n",
    "w2 = (1 - w1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The PyMC3 model.  Note that we are making two gaussians, where one has `w1` (90%) of the mass:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sample initial stage: ...\n",
      "Stage: 0 Beta: 0.010 Steps: 25\n",
      "Stage: 1 Beta: 0.029 Steps: 11\n",
      "Stage: 2 Beta: 0.064 Steps: 2\n",
      "Stage: 3 Beta: 0.136 Steps: 9\n",
      "Stage: 4 Beta: 0.289 Steps: 3\n",
      "Stage: 5 Beta: 0.603 Steps: 13\n",
      "Stage: 6 Beta: 1.000 Steps: 3\n"
     ]
    }
   ],
   "source": [
    "def two_gaussians(x):\n",
    "    log_like1 = - 0.5 * n * tt.log(2 * np.pi) \\\n",
    "                - 0.5 * tt.log(dsigma) \\\n",
    "                - 0.5 * (x - mu1).T.dot(isigma).dot(x - mu1)\n",
    "    log_like2 = - 0.5 * n * tt.log(2 * np.pi) \\\n",
    "                - 0.5 * tt.log(dsigma) \\\n",
    "                - 0.5 * (x - mu2).T.dot(isigma).dot(x - mu2)\n",
    "    return tt.log(w1 * tt.exp(log_like1) + w2 * tt.exp(log_like2))\n",
    "\n",
    "\n",
    "with pm.Model() as model:\n",
    "    X = pm.Uniform('X',\n",
    "                   shape=n,\n",
    "                   lower=-2. * np.ones_like(mu1),\n",
    "                   upper=2. * np.ones_like(mu1),\n",
    "                   testval=-1. * np.ones_like(mu1))\n",
    "    llk = pm.Potential('llk', two_gaussians(X))\n",
    "    trace = pm.sample_smc(2000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the results using the traceplot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
